Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 227–244 | Cite as

On quantitative uniqueness for elliptic equations

  • Guher Camliyurt
  • Igor KukavicaEmail author
  • Fei Wang


We address the question of quantitative uniqueness for the equation \(\Delta u=V u\) with either periodic or Dirichlet boundary conditions in a disk. We construct solutions u corresponding to potential functions V such that u vanishes of order \(\mathrm{const} \Vert V\Vert _{L^\infty }^{2/3}\). The example also shows sharpness of recently obtained bounds in the case of a parabolic equation \(u_t-\Delta u= V u\).



The authors were supported in part by the NSF Grant DMS-1615239.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

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